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Title: The Heart of Mathematics: An Invitation to Effective Thinking by Edward B. Burger, Michael Starbird ISBN: 1-55953-407-9 Publisher: Key Curriculum Press Pub. Date: April, 2000 Format: Hardcover Volumes: 1 List Price(USD): $69.95 |
Average Customer Rating: 4.5 (4 reviews)
Rating: 3
Summary: Disturbing to say the least
Comment: Dear Authors of The Art of Mathematics:
Hi, I don't know how to start this letter
I am a friendly person who likes to build people up, and likes helping people
I offered my help to a new friend, who just started attending SJSU
Since she has no math background, she had to take a basic math course.
I have a BS in Chemistry/Nuclear Physics from SJSU
I have tutored hundreds of students, in mathematics, physics, chemistry,
spanish, etc
And I had to warn so many students about the lack of touch with reality of some
college Professors, and their lack of guidance to students in how to prepare
themselves to succeed in college.
For instance, I would warn them that organic chemistry is different than general
chemistry, and that usually college professors would never warn the students
that they are trying to cramp too much knowledge too soon, and specially with
organic chemistry, that they will be ill prepared if they didn't start studying
before they take the class
I have helped in several University programs, like EOPS, Upward bound, Summer
Bridge, Alliance for minority participation, Minority engineering program, etc
And I have met so many professors who are unhelpful and out of touch with the
reality of the difficulty of mastering any concepts
For instance, electricity and magnetism, Maxwell's equations, etc,
Students get discouraged because they can't see what is going on, and no one
seems to remind them that what it took scholars decades to master, they are
asked to understand in a semester
Well, when I went to help my new friend, and she shows me she has to prove
Cantor's method for ... I was shocked...
I love mathematics, it is not my major, but I have loved the process of
reflexion that this science has brought to my mind
But I find it SO DISTURBING that a friend who has never taken any geometry, or
trigonometry, or basic logic, etc, etc, is thrown into trying to prove something
that, again, it took scholars decades to understand
I see it everywhere in the academic world
It is SO EASY to forget how hard it is not to understand
I read an article written in the seventies, in a journal of Chemistry, about the
margin of excellence
The whole article was about how the margin of excellence was being lost, because
of the need to expose undergraduates to as much knowledge as possible (without a
true mastery or understanding of it)
I think few students will have the courage to express their minds and/or able to
see that maybe the purpose of the book was the self agrandizemnt of its authors
Students ask the professor for a deeper explananation, which the same professor
can't provide
Then students find themselves regurgitating the answer given to them, and fake a
true understanding to pass the class
I love mathematics, but just to see a water down introduction to deep concepts
of mathematics, and the exposure of these concepts to students who may or may
not have the intellectual skills (for the lack of formal mathematical classes)
is disturbing to me.
Please, please, please, send spies into the classrooms of people taken this
course and be willing to hear the true opinions of students
Best of life to you
Sincerely
Rating: 5
Summary: An Unusual Book of Wide Interest
Comment: The Heart of Mathematics is an unconventional math survey aimed primarily at social science and humanities students. While students in "soft" majors are the primary intended audience, math majors and others who have already progressed beyond the introductory level are likely to find this book of great interest as well.
The book gives readers a good feel for the variety of problems that mathematicians tackle. In fact, one of the book's great strengths is the range of topics it covers, from number theory and games, to topology, to chaos and fractals. It does this with little use of conventional mathematical notation or jargon, and the level of presentation is so elementary that the book can be "read" just as any non-technical book can be read. At the same time, the authors go to great lengths to encourage reader participation. Many hands-on demonstrations and experiments are provided, and the end-of-chapter exercises ask readers to discuss the material with others and write about their experiences.
The topics presented are fascinating. I read this book on my vacation and found several passages to read to my wife and daughter almost every day. (This provided a lot of amusement for everyone when my 12-year-old daughter would solve problems in a few seconds that I had been pondering without much success.)
The book's subtitle is "An Invitation to Effective Thinking," and the authors present problem-solving strategies that can be applied to problems within and outside the field of mathematics. While readers will no doubt be familiar with many of them already, it is difficult for me to imagine anyone who would not benefit from at least some of the strategies presented.
The authors' writing is very informal with a lot of corny humor - possibly too much for a lot of people - but at the same time you do get a sense of the authors as good guys who know some important things and want to share the wealth.
In summary, this is a most unusual and stimulating book. Highly recommended.
Rating: 5
Summary: interesting read
Comment: Dr. Starbird teaches my number theory course. Just needing to fulfill requirements, I'm taking the course as a wash (I've already had the more advanced courses). I figured since he saved us money by not requiring a text, I could spend the money to check out his (co-authored) book.
It's well worth the money ... and, at best, will enrich your daily thought process. At worst, if you are a student of mathematics, it will at least help you along in the more abstract approaches, giving you a basis and idea of the thought process mathematicians use to approach problems. I wish I had encountered it as a freshman!
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Title: How the Other Half Thinks: Adventures in Mathematical Reasoning by Sherman Stein ISBN: 0071407987 Publisher: McGraw-Hill/Contemporary Books Pub. Date: 01 August, 2002 List Price(USD): $10.95 |
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Title: Journey Through Genius: The Great Theorems of Mathematics by William Dunham ISBN: 014014739X Publisher: Penguin USA (Paper) Pub. Date: August, 1991 List Price(USD): $14.95 |
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Title: The History of the Calculus and Its Conceptual Development by Carl B. Boyer ISBN: 0486605094 Publisher: Dover Pubns Pub. Date: 01 June, 1959 List Price(USD): $11.95 |
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Title: Calculus : An Intuitive and Physical Approach (Second Edition) by Morris Kline ISBN: 0486404536 Publisher: Dover Pubns Pub. Date: 12 November, 1998 List Price(USD): $26.95 |
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Title: Calculus With Analytic Geometry by George Finlay Simmons ISBN: 0070576424 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 October, 1995 List Price(USD): $99.69 |
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